The power line to your outlets should never be less than #12 in order to maintain the 20-amp (max) rating. Most commercial grade #12 wiring is THHN solid core copper. If you buy a cord with #10's, then you are effectively limiting the power draw to your equipment (conversely, it also makes sense that cord gages fatter than #12 do nothing to improve power flow from the incoming service to the user).
As far as stranded vs solid core, the only difference is the solid core wires have a lower resistivity per foot than stranded - which is why power wiring is usually specified as solid core.
Here's where I get in trouble: power cords with gages equal or bigger than the power wiring size do nothing to improve the sound of your system with respect to current flow; the sonic differences are the result of shielding RFI/EMI only. The PVC insulation, copper purity, etc. might make a difference with respect to signal carrying; however there's no effect on power delivery.
As far as stranded vs solid core, the only difference is the solid core wires have a lower resistivity per foot than stranded - which is why power wiring is usually specified as solid core.
Here's where I get in trouble: power cords with gages equal or bigger than the power wiring size do nothing to improve the sound of your system with respect to current flow; the sonic differences are the result of shielding RFI/EMI only. The PVC insulation, copper purity, etc. might make a difference with respect to signal carrying; however there's no effect on power delivery.